Details

sample34.0ms

Algorithm

intervals

Results

24.0ms

256×

body

valid

simplify124.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	9
1	51	9
2	69	9
3	86	9
4	94	9
5	105	9
6	139	9
7	177	9
8	202	9
9	246	9
10	416	9
11	615	9
12	992	9
13	1948	9
14	2240	9
15	3154	9
16	5001	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)
0.0b	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
0.1b	(* x (+ 0.99229 (* x 0.04481)))
16.9b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
16×	`add-cube-cbrt`
11×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r`
8×	`pow1`
6×	`associate-l` `add-log-exp`
4×	`associate-*r/` `difference-of-squares`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 95

Calls

4 calls:

30.0ms	(- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)
68.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
7.0ms	(* x (+ 0.99229 (* x 0.04481)))
9.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)
94.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
64.0ms	(* x (+ 0.99229 (* x 0.04481)))
57.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	524	1067
1	2237	989
2	5001	989

prune238.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.70711 (- (/ 1 (/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061)))) x))
0.1b	(* x (+ 0.99229 (* x 0.04481)))
0.2b	(/ 1 (/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061))))
16.9b	(/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
78×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
60×	`add-cube-cbrt`
21×	`add-exp-log`
18×	`associate-/r*`
15×	`add-cbrt-cube`
13×	`associate-r`
11×	`associate-/r/`
9×	`pow1`
8×	`div-exp`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-l` `associate-/l*`
5×	`difference-of-squares`
4×	`cbrt-undiv` `associate-*r/` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `rec-exp` `frac-2neg` `1-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `unswap-sqr`
1×	`flip3--` `pow-flip` `flip--` `inv-pow`

Counts

4 → 168

Calls

4 calls:

127.0ms	(* 0.70711 (- (/ 1 (/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061)))) x))
7.0ms	(* x (+ 0.99229 (* x 0.04481)))
12.0ms	(/ 1 (/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061))))
10.0ms	(/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* 0.70711 (- (/ 1 (/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061)))) x))
67.0ms	(* x (+ 0.99229 (* x 0.04481)))
62.0ms	(/ 1 (/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061))))
54.0ms	(/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061)))

simplify95.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	804	2202
1	3892	1937
2	5002	1934

prune339.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061))))
0.0b	(log (exp (/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061)))))
0.1b	(* x (+ 0.99229 (* x 0.04481)))
16.9b	(/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
30×	`exp-prod`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
16×	`log-pow`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r/`
5×	`flip3-+` `flip-+` `add-log-exp`
3×	`log-prod` `associate-r` `associate-l` `associate-/r` `div-inv` `associate-/l`
2×	`associate-*r/` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 103

Calls

4 calls:

12.0ms	(exp (/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061))))
13.0ms	(log (exp (/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061)))))
7.0ms	(* x (+ 0.99229 (* x 0.04481)))
10.0ms	(/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(exp (/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061))))
52.0ms	(log (exp (/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061)))))
62.0ms	(* x (+ 0.99229 (* x 0.04481)))
55.0ms	(/ (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))) (+ 2.30753 (* x 0.27061)))

simplify56.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	432	1058
1	1757	972
2	5001	971

prune361.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (- (+ (* 0.37920088514346545 x) 0.4333638132548656) (* 0.02505083423776644 (pow x 2)))) x)
0.0b	(- (+ (* 0.37920088514346545 x) 0.4333638132548656) (* 0.02505083423776644 (pow x 2)))
0.1b	(* 0.02505083423776644 (pow x 2))
0.2b	(/ 1 (- (+ (* 0.37920088514346545 x) 0.4333638132548656) (* 0.02505083423776644 (pow x 2))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`add-exp-log`
11×	`times-frac` `add-log-exp`
8×	`associate-r` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `unswap-sqr`
3×	`flip3--` `diff-log` `associate-l` `prod-exp` `associate-/r` `flip--` `associate-/l` `difference-of-squares`
2×	`sub-neg` `div-exp` `associate-/r/` `div-inv` `distribute-lft-out--` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `pow-flip` `frac-2neg` `1-exp` `pow-exp` `associate--l+` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 91

Calls

4 calls:

100.0ms	(- (/ 1 (- (+ (* 0.37920088514346545 x) 0.4333638132548656) (* 0.02505083423776644 (pow x 2)))) x)
19.0ms	(- (+ (* 0.37920088514346545 x) 0.4333638132548656) (* 0.02505083423776644 (pow x 2)))
5.0ms	(* 0.02505083423776644 (pow x 2))
19.0ms	(/ 1 (- (+ (* 0.37920088514346545 x) 0.4333638132548656) (* 0.02505083423776644 (pow x 2))))

series140.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (/ 1 (- (+ (* 0.37920088514346545 x) 0.4333638132548656) (* 0.02505083423776644 (pow x 2)))) x)
23.0ms	(- (+ (* 0.37920088514346545 x) 0.4333638132548656) (* 0.02505083423776644 (pow x 2)))
29.0ms	(* 0.02505083423776644 (pow x 2))
45.0ms	(/ 1 (- (+ (* 0.37920088514346545 x) 0.4333638132548656) (* 0.02505083423776644 (pow x 2))))

simplify54.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	381	811
1	1535	735
2	5001	726

prune196.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes12.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	12
1	29	12

end0.0ms

sample740.0ms

Algorithm

intervals

Results

643.0ms

8000×

body

valid